Question

Assume that gold has one electron per atom to carry charge. The mass density of gold is 1.89×104 kg/m3 and its molecular weight is 197.0 g/mol. Calculate the drift speed of the electrons in a wire made of gold, with a radius of 0.57 mm, that carries a current of 1.36 A.

Answer 1

There is one electron per atom present in gold. Thus, gold is a monovalent atom The current density is defined as the ration of the current per unit area, that is, 1.36 A 136 A 3.14(057x103 m -1.33x106 A/m2 The current density in term of the drift velocity is as follows J =neAlvd Here, n is the atomic density.eis the charge of electron, A is the area of then wire, Iis the current flowing in the wire, and v is the drift velocity. The atomic density is, A. Here, Ma is the Avogadro number, Pa is the mass density, and MA is the molecular weight (6.022x 1026)(1.89 x 104) n- 1.97x10 0.058x1033 Now, the drift velocity is as follows ne 1.33x105 A/m' (0.058x10") (1.6x1019)(3.14) (0.57x103 m) (1.36A) 10.23×10-2 m/s -0102 m/s

Answer 2

Drift velocity is,

v = l / q*A

where l = current

q = charge density

A = area = pi*r^2

Molar density = 1.89*10^7 / 197 = 95939.086 mol/m^3

Atomic density = 95939.086 * 6.02*10^23 = 5.77*10^28 atoms/m^3

Charge density q = 5.77*10^28*1.6*10^(-19) = 9.24*10^9 C/^3

Drift velocity v = 1.36 / 9.24*10^9*pi*(0.57*10^(-3))^2

v = 4.53*10^(-4) m/s

Answer